This statement is the report of a workshop: “Enhancing internationally competitive research in Europe’s universities.” Research-intensive universities are seen as the principal agents of basic research in Europe. To realise its full potential different actions should be initiated: it will require e.g. a more competitive research funding environment and a focus on a cohort of young, world class researchers. The framework for these developments should be the creation of a European Common Market for Research. LERU also included a list of recommendations, followed by the appendices.